Evaluation of Microirrigation Uniformity on Laterals Considering Field Slopes

Water application uniformity is an important performance criterion that must be considered during the design and evaluation of the microirrigation systems. This study was conducted to evaluate the water application uniformity considering field slopes. The uniformity parameters including coefficient of variation (CV), Christiansen’s uniformity coefficient (UCC), distribution uniformity (DU), emitter discharge variation qv(q?max) expressed by the difference between the maximum emitter flow rate qmax and the minimum emitter flow rate qmin to qmax, emitter discharge variation qv(qd) expressed by the difference between qmax and qmin to design emitter flow rate qd, emitter discharge variation qv(qd) expressed by the difference between qmax and qmin to average emitter flow rate q(avg), emission uniformity (EU(q?avg)) expressed by qmin to qavg, and EU(qd) expressed by qmin to qd. Furthermore, the relationships of CV versus UCC, CV versus DU, CV versus qv(qd), CV versus qv(q?max), CV versus qv(q?avg), CV versus EU(q?avg), and CV versus EU(qd) were also discussed. The results of the study revealed that the field slope does not obviously affect the relationships of CV versus UCC, CV versus qv(q?max), and CV versus qv(q?avg) for any of the slopes evaluated, which include uphill, zero slope, and downhill. Furthermore, the effect of slope on the relationships of CV versus EU(q?avg), CV versus EU(qd), and CV versus qv(qd) was obvious, especially when large downhill slopes with a CV>0.05 were considered. However, the effect of slope on the relationships of CV versus DU was intermediate. Taken together, the results of this study indicated that the UCC, qv(q?max), and qv(q?avg) should be recommend in addition to CV when evaluating the water application uniformity of the microirrigation systems, regardless of slope, and that qv(qd) and EU(qd) should be recommend when evaluating systems placed in fields with a slope of zero or an uphill slope.     

Computing Inlet Pressure Head of Multioutlet Pipeline

Expressions for the factor K to relate the total frictional head loss, average outlet operating pressure head, and the inlet pressure head of a multioutlet pipeline are developed. In the developed expressions, the factor K is a function of the number of outlets on different pipe diameters, combination of diameters, and position of the first outlet from the inlet. Values of the factor K obtained from the developed expressions are compared with constant values being taken as per existing practice. The comparison suggests using the developed expressions for accurate computation of the factor K for multioutlet pipelines especially comprising of two or more diameters. An example is presented to compute the inlet pressure head of a multioutlet pipeline using the factor K.     

Analytical Equation for Variation of Discharge in Drip Irrigation Laterals

Statistical uniformity of discharge variation is an important parameter in designing drip irrigation laterals. A simple analytical equation is derived to determine the coefficient of variation of discharge. This equation is used to determine the coefficient of variation of discharge for a numerical problem. The result is compared with the energy gradient line approach. Both the methods give the same result. For any required coefficient of variation of discharge, the diameter of a lateral can be designed directly for a known lateral length, slope, emitter discharge exponent, pressure head at the start of the lateral, and discharge rate through the lateral, by writing the analytical equation in quadratic form.     

Microirrigation Submain Unit with Pressure Reducing Pipes

A pressure reducing pipe (PRP), used at the inlet of a lateral in microirrigation systems to improve water application uniformity, is developed. It is composed of an internal spiral and a sleeve pipe and is made of molded polyethylene plastic. It functions to dissipate a pressure head that exceeds the required pressure head of a lateral inlet by directing water flow through the spiral grooved path and creating a certain head loss. An improved design method for submain units using the pressure reducing pipes is based on the hydraulics of the submain unit and the characteristics of the head loss in the PRP. The effects of the PRP on water application uniformity in a submain unit are analyzed by computer simulation. The submain unit with the PRP has higher uniformity than that of the commonly used method. After choosing the PRP, the permissible range of pressure variation in a submain will not need to be considered for the submain length in a layout.     

Optimal Design of Pressurized Irrigation Subunit

A linear programming (LP) model is presented for optimal design of the pressurized irrigation system subunit. The objective function of the LP is to minimize the equivalent annual fixed cost of pipe network of the irrigation system and its annual operating energy cost. The hydraulic characteristics in the irrigation subunit are ensured by using the length, energy conservation, and pressure head constraints. The input data are the system layout, segment-wise cost and hydraulic gradients in all the alternative pipe diameters, and energy cost per unit head of pumping water through the pipeline network. The output data are: segment-wise lengths of different diameters, operating inlet pressure head, and equivalent annual cost of the pipeline network. The explicit optimal design is demonstrated with design examples on lateral and submain or manifold of pressurized irrigation systems. The effect of the equations for friction head loss calculation on optimization procedure is investigated through the design example for microirrigation manifold. The performance evaluation of the proposed model in comparison with the analytical methods, graphical methods, numerical solutions, and dynamic programming optimization model reveals the good performance of the proposed model. The verification of operating inlet pressure head obtained by the proposed model with accurate numerical step-by-step method suggested that it is mostly accurate.     

Inlet Pressure, Energy Cost, and Economic Design of Tapered Irrigation Submains

A new particularly simple equation is derived to solve explicitly the economic design problem of submain lines (microirrigation manifold and sprinkle irrigation submains) with pumping. The appropriate lengths of the submain line segments with different diameters are directly calculated from the proposed equation in such a way the total cost of energy and pipes is minimized. It is shown that the portion of energy cost affected by changes in the submain pipe sizes is proportional to the inlet pressure head of the submain. A new equation is derived relating the inlet pressure head of a tapered multioutlet pipeline to the average pressure head value. Direct design solutions were obtained for two different cases ensuring two different hydraulic conditions. In the first case, the average value of outflow over all the outlets (emitters) of the system is imposed to be identical to the required average outlet discharge. This implies that the average pressure head value in the submain is imposed to be equal to an a priori known constant. In the second case the energy cost is assumed proportional to the friction losses along the submain. The explicit economic design is demonstrated in two design examples. Comparisons with previous methods and numerical models indicated the good performance of the suggested solution.     

Water Distribution in Laterals and Units of Subsurface Drip Irrigation. II: Field Evaluation

The performance of drip irrigation and subsurface drip irrigation (SDI) laterals has been compared. Two emitter models (one compensating and the other noncompensating) were assessed. Field tests were carried out with a pair of laterals working at the same inlet pressure. A procedure was developed that recorded head pressures at both lateral extremes and inlet flow during irrigation. Both models showed similar behavior and soil properties affected their discharge. On the other hand, the performance of a field SDI unit of compensating emitters was characterized by measuring pressures at different points and inlet flow. Finally, the distribution of water and soil pressure in the laterals and the unit were predicted and irrigation uniformity and soil pressure variability were also determined. Predictions agreed reasonably well with the experimental observations. Thus, the methodology proposed could be used to support the decision making for the design and management of SDI systems.     

New Computational Fluid Dynamic Procedure to Estimate Friction and Local Losses in Coextruded Drip Laterals

The design of trickle irrigation systems is crucial to optimize profitability and to warrant high values for the emission uniformity (EU) coefficient. EU depends on variation of the pressure head due to head losses along the lines and elevation changes, as well as the water temperature, and other parameters related to the emitters (manufacturer’s coefficient of variation, number of emitters per plants, emitter spacing). Trickle irrigation plants are usually designed using small diameter plastic pipes (polyethylene or polyvinyl chloride). The design problem, therefore, needs to consider head losses along the lines as well as emitter discharge variations due to the manufacturer’s variability. Variations in the hydraulic head are a consequence of both friction losses along the pipe and local losses due to the emitters’ connections, whose importance has been recently emphasized. Since each local loss depends on the emitter type (in-line or on-line) as well as on its shape and dimensions, the morphological variability of the commercially available emitter requires experimental investigations to determine local losses in drip laterals. On the other hand, local losses can be estimated by the mean of computational fluid dynamics (CFD) models, allowing analysis of velocity profiles and the turbulence caused by the emitters’ connections. FLUENT software can be considered a powerful tool to evaluate friction and local losses in drip irrigation laterals, after the necessary validation has been carried out by means of experimental data. The main objective of this study was to assess a CFD technique to evaluate friction and local losses in laterals with in-line coextruded emitters. The model was initially used to choose the turbulence model allowing the most accurate estimation of friction losses in small diameter polyethylene pipes, characterized by low Reynolds number. Second, the possibility of using CFD to predict local losses in drip irrigation laterals with a commercially available coextruded emitter was investigated. Simulated local losses were obtained as difference of the total and friction losses along a trunk of pipe, where one single emitter was installed, not considering the emitter outflow. The proposed procedure allows to evaluate local losses for other different emitter models, avoiding tedious and time-consuming experiments.     

Microirrigation Lateral Design using Lateral Discharge Equation

A simple and accurate method is developed for designing single, paired, and tapered microirrigation laterals. The hydraulics of the lateral is evaluated using a lateral discharge equation approach. A simple power equation is used to express the relationship between the inlet flow rate and inlet pressure head of the lateral. Keeping the flow variation within the specified limit, a procedure for designing the length of the tapered section is developed. The lateral is designed using a step-by-step method. The length of the tapered section is determined by the golden section search method.     

Linear Solution for Hydraulic Analysis of Tapered Microirrigation Laterals

A simplified analytical solution that takes into account the effect of the emitter discharge exponent on the hydraulic computations of tapered microirrigation laterals, is presented. The hydraulic analysis is evaluated based on the spatially variable discharge function approach. A simple power equation was used to express distribution of the variable outflow delivered from the each emitter along the lateral. An analytical solution is developed for the case of a linear relationship between the emitter discharge and pressure head, namely, the emitter discharge exponent equals to unique, y = 1.0. In this procedure, the analytical derivations can be applied for uphill, downhill, and zero slope conditions. Results are comparable to those obtained from the literature.     

Water Distribution in Laterals and Units of Subsurface Drip Irrigation. I: Simulation

A complete methodology to predict water distribution in laterals and units of subsurface drip irrigation (SDI) is proposed. Two computer programs have been developed for the hydraulic characterization of SDI; one for laterals and the other for units. Emitter discharge was considered to depend on hydraulic variability, emitter’s manufacture and wear variation, and soil pressure variation. A new procedure to solve the hydraulic calculation of SDI looped network has been established. Moreover, spatial distribution of soil variability was estimated by a geostatistical modeling software that is coupled with the computer programs. Thus the evaluation and performance of laterals and units of SDI can be addressed by changing input variables such us: length and diameters of laterals; coefficients of emitter’s discharge equation; coefficient of variation of emitter’s manufacture and wear; local losses at the emitter insertion; inlet pressure; and soil hydraulic properties and its spatial variability. Finally, the methodology has been applied to different scenarios, and some recommendations are outlined for the selection of emitter discharge and inlet pressures.     

Continuous Outflow Variation along Irrigation Laterals: Effect of the Number of Outlets

Previous continuous-uniform outlet discharge approaches for the hydraulic analysis of irrigation laterals are generally valid for large (theoretically) infinite number of outlets. For a finite number of outlets, however, these approaches may lead to errors in hydraulic computation. A new continuous-uniform outflow approach that takes into account the effect of the number of outlets on the lateral hydraulics is presented. A new analytical equation describing the energy line shape along uniform sprinkle and trickle irrigation laterals and manifolds is developed. The effect of ground slope and velocity head on hydraulic computation is also considered. The method is however restricted by the simplified assumption of equal outlet discharge. An alternate improved analytical method considering the effect of non-uniform outflow distribution along the lateral is also included. Analytical expressions for determining the inlet pressure head and global statistical parameters characterizing the outflow distribution (Christiansen uniformity coefficient, pressure head variation) are developed for design and evaluation purposes. Comparison tests with an accurate numerical stepwise method indicated that the proposed simplified approach is more accurate than other previous works particularly when the number of outlets is relatively small. The improved method is the most accurate method for all cases examined even for low levels of uniformity.     

Determining Minor Head Losses in Drip Irrigation Laterals. I: Methodology

Minor head losses at emitter insertions along drip laterals were predicted by a derivation of Bélanger’s theorem and analyzed by the classic formula that includes a friction coefficient K multiplied by a kinetic energy term. A relationship was established for K as a function of some emitter geometric characteristics. These take into account the flow expansion behind the reduction of the cross-sectional area of the pipe due to obstruction by the emitter. Flow constrictions at emitter insertions were estimated by analogy with contraction produced by water jets discharging through orifices. An experimental procedure was also developed to determine minor losses in situ, in the laboratory or in the field. An approach is suggested to calculate either K or the emitter equivalent length le as a function of lateral head losses, inlet head, and flow rate. Internal diameter and length of lateral, emitter spacing, emitter discharge equation, and water viscosity must be known. Approximate analytical relations to study flow in laterals were developed. They may be used to design and evaluate drip irrigation units. Analytical and experimental procedures are validated in the companion paper by Juana et al.     

Soil Hydraulic Properties Affecting Discharge Uniformity of Gravity-Fed Subsurface Drip Irrigation Systems

The use of subsurface drip irrigation (SDI) is increasing for many reasons, including its many agronomic advantages and the ability for safe application of wastewater to crops. In contrast to surface drip irrigation, soil hydraulic properties may affect SDI performance, particularly for new SDI systems designed to operate under low pressure (e.g., 2?m of head). This work introduces a new approach for solving problems of predicting discharge in SDI laterals. We accomplish this by coupling models of head loss in laterals and soil impacts on dripper discharge. The coupled model enables an evaluation of the performance of SDI laterals while changing inputs, such as the lateral diameter, length and slope, dripper nominal discharge and exponent, inlet pressure head, soil hydraulic properties, and soil spatial variability. This model is used to determine the coefficient of variation of discharge for two numerical comparisons.     

Experimental Analysis of Local Pressure Losses for Microirrigation Laterals

The accurate design of drip irrigation laterals needs to consider the variation of hydraulic head due to pipe elevation changes, head losses along the lines, and also, at a given operating pressure, emitter discharge variations related to manufacturing variability, clogging, and water temperature. Hydraulic head variations are consequent to both the friction losses and local losses due to the in-line or on-line emitters along the pipe, which determine the contraction and subsequent enlargement of the flow streamlines. Moreover, in-line emitters usually have a smaller diameter than the pipe, and therefore an additional friction loss must be considered. Evaluation of energy losses and consequently the design of drip irrigation lines is usually carried out by assuming the hypothesis that local losses can be neglected, even if previous experimental researches showed that local losses can become a significant percentage of total head losses as a consequence of the high number of emitters installed along the lines. This paper reports the results of an experimental investigation to evaluate local losses in integrated laterals in which coextruded emitters are installed inside the pipe. Local losses were measured for 10 different types of commercially available integrated laterals and for different Reynolds numbers. A practical power relationship was deduced between the α coefficient, expressing the amount of local losses as a fraction of the kinetic head, and a simple geometric parameter characterizing the geometry of the emitter and the pipe. Local losses obtained for integrated laterals were then compared with those due to the on-line emitters, previously determined as a function of the pipe-emitter geometry. The proposed criterion for calculating the local losses was finally verified by using a step-by-step procedure.     

Compatibility Assessment of Drip Irrigation Laterals

Emitters inserted in drip irrigation laterals cause local head loss, generally estimated as a product of a coefficient and the velocity head. This local head loss coefficient and the emitter discharge curve hydraulic parameters may exhibit considerable variability attributable to the manufacturing process. This paper provides a framework for assessing whether the variability in the hydraulic parameters could lead to significant differences in the performance of rolls of drip irrigation laterals from the same manufacturing batch. A system approach with inlet pressure as input, pressure distribution along the drip lateral and inlet discharge as outputs (or responses), and a drip lateral hydraulic model as the transfer function is explored. Within a Bayesian statistical framework of parameter uncertainty based on the Metropolis algorithm, the hydraulic parameters of pressure-compensating drip lateral rolls from the same manufacturing batch were inferred (calibrated). Overlapping of the space (region) of the hydraulic parameters of different drip laterals give an indication of compatibility (similarity) of the drip laterals. Results indicated that half of the drip lateral rolls tested were strongly compatible, a third were weakly compatible, and the remainder were not compatible with any other. This finding has significant ramifications in the design of drip irrigation lateral networks. Therefore, it is essential to closely examine the hydraulic properties of drip laterals for the design of drip irrigation networks to avoid poor performance of the system.     

Rapid Evaluations of Anticlogging Performance of Drip Emitters by Laboratorial Short-Cycle Tests

Emitter clogging is the most annoying problem that restrains the development of drip irrigation technologies, but so far, there have been no effective evaluation methods for the anticlogging performance of drip emitters. In this study, a kind of short-cycle experiment was conducted in the laboratory by mixing sands with various concentrates and particle sizes in irrigation water. Through these tests, the clogging rates that quantitatively represent the clogging status of drip emitters in various experimental conditions were obtained, as well as the variation rules of emitter discharges. The statistical calculation results indicated that the anticlogging performance of predepositing drippers was better than round-flow drip tapes, but less than eddy drip arrows. The discharges of every emitter tested differed from each other and most were lower than nominal discharge rates. However, a few emitters had a contrary result. An important modification had been done for the Christiansen uniformity coefficient to accurately evaluate irrigation uniformity and the clogging status of drip emitters. As a result, a new method of rapid evaluation for the anticlogging performance of drip emitters was proposed.     

Optimum Design of Microirrigation Systems in Sloping Lands

When an area to be irrigated has a high slope gradient in the manifold line direction, an option is to use a tapered pipeline to economize on pipe costs and to keep pressure head variations within desired limits. The objective of this paper is to develop a linear optimization model to design a microirrigation system with tapered, downhill manifold lines, minimizing the equivalent annual cost of the hydraulic network and the annual pumping cost, and maximizing the emission uniformity previously established to the subunit. The input data are irrigation system layout, cost of all hydraulic network components, and electricity price. The output data are equivalent annual cost, pipeline diameter in each line of the system, pressure head in each node, and total operating pressure head. To illustrate its capability, the model is applied in a citrus orchard in S?o Paulo State, Brazil, considering slopes of 3, 6, and 9%. The model proved to be efficient in the design of the irrigation system in terms of the emission uniformity desired.     

Experimental Determination of the Hydraulic Properties of Low-Pressure, Lay-Flat Drip Irrigation Systems

The hydraulics of IDEal low-pressure drip irrigation system components were analyzed under controlled laboratory conditions. The hydraulic loss coefficient for the lateral-submain connector valves was determined based on laboratory measurements. It was found that the hydraulic loss due to friction in the lay-flat laterals can be accurately estimated with standard friction loss equations using a smaller effective diameter based on the wall thickness and inlet pressure head. The equivalent-length barb loss, expressed as an equivalent length of lateral, was calculated for button emitters, as well as for microtubes inserted to lengths of 5 and 10 cm. The head-discharge relationship and coefficient of manufacturer’s variation of prepunched lateral holes (without emitters), button emitters, and microtubes were determined. It was found that most of the head loss occurs in the connector valve, which has a relatively small hole through the hollow stopcock. The presence of manufacturing debris in the valve also increases the head loss and contributes to variability in the valve loss coefficient. The lateral cross-sectional area in the creases does not greatly impact the effective diameter for the 125-, 200-, and 250-μm wall thickness laterals. However, the use of the lateral height as effective diameter for the 500-μm sample resulted in significant overestimation of friction loss. The prepunched holes and the button emitters had very low manufacturer’s variation coefficients, but the microtube emitters showed excellent uniformity and are the emitter of choice among the tested alternatives. However, the microtube flow rate is relatively high and is more sensitive to pressure variation than the other emitter types.     

Field-Scale Assessment of Uncertainties in Drip Irrigation Lateral Parameters

Grass establishment on railway embankment steep slopes for erosion control in Central Queensland, Australia, is aided by drip lateral irrigation systems. The effective field values of the lateral parameters may be different from the manufacturer supplied ones due to manufacturing variations of the emitters, environmental factors, and water quality. This paper has provided a methodology for estimating drip lateral effective parameter values under field conditions. The hydraulic model takes into account the velocity head change and a proper selection of the friction coefficient formula based on the Reynolds number. Fittings and emitter insertion head losses were incorporated into the hydraulic model. Pressure measurements at some locations within the irrigation system, and the inlet discharges, were used to calibrate the lateral parameters in a statistical framework that allows estimation of parameter uncertainties using the Metropolis algorithm. It is observed that the manufacturer’s supplied parameters were significantly different from the calibrated ones, underestimating pressures within the irrigation system for a given inlet discharge, stressing the need for field testing. The parameter posterior distributions were found to be unimodal and nearly normally distributed. The emitter head loss coefficient distribution being very significant suggests the need to incorporate it into the hydraulic modeling. Although the example given in this paper relates to steep slopes, the methodologies are general and can be applied to any use of drip laterals.